Eight Balls, One Heavier
The puzzle
You have eight balls that look identical. Seven weigh the same and one is slightly heavier.
You have a balance scale - the kind with two pans that tells you which side is heavier, or that they are equal. You may use it twice. Find the heavy ball.
Stuck?
One at a time, smallest first. Open only as many as you need — the whole point of the puzzle is the part you work out yourself.
Hint 1
Splitting into two fours wastes the scale’s third answer. What is it?
Hint 2
A weighing has three possible results. How many balls can two weighings distinguish?
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Split them 3, 3 and 2. Weigh the two threes; if they balance the heavy ball is in the pair, and one weighing finds it. If one three is heavier, weigh two of its balls against each other.
How to get there
Divide the balls into groups of three, three and two. Put the two threes on the pans.
If they balance, the heavy ball is one of the two set aside. Weigh those two against each other and the heavier pan holds it. Two weighings.
If one side is heavier, the heavy ball is among those three. Take any two of them and weigh one against the other: if one is heavier that is the ball, and if they balance it is the third. Again two weighings.
The technique worth keeping
A balance has three outcomes, not two, so a weighing divides the possibilities by three rather than by two - two weighings separate up to nine cases. Splitting eight into two fours throws away the "balanced" result and leaves you needing three. Always count the outcomes before choosing the split.